range constants in gage rr calculations

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    could someone please explain how the range constants are derived mathematically in the calculations embedded in excel gage r&r worksheets?
    specifically: in repeatability studies, the constant k1=4.56 or k1=3.05 is used as a range multiplier if there are 2 or 3 trials, respectively…
    similarly, in reroducibility studies, the constant k2=3.65 or k2=2.7 is used as a factor if there are 2 0r 3 operators, respectively…
    where do k1 and k2 come from?



    k1 and k2 are used to calculate the width of your measurement error band. Say if you wish to create a band around a metric, how do you do it? Well, you calculate the control limits (or in other words 6 std deviations). This is what precisely k1 and k2 help you do. They are nothing but multiplication of 5.15 times (for 99% confidence) the Rbar divided by d2 (std devn from the control chart theory) d2 depends on your sample size. So for repeatability what would be your sample size (i.e. how many readings do you take for each combination of part and operator). The answer is number of trials so if the number of trials is 2 then you can pick the d2 figure for sample size 2. You can do the calculation manually and check the figures.
    Reproducibility is not that straight forward. I suggest going through some books might give you more clarity.
    Hope this was helpful..

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